Bathtub FItting Analysis Question 1

[aerohead56]

I have come across some tension fitting analysis that seems to misuse the assumptions of Lockheed Stress Memo No 88a. The analysis uses an angle type fitting and arrives at a value for the variable d that is negative. Since this means that the hole actually lies outside the theoretically constructed semi-circular fitting is it in error? Or, since the theoretical semi-circular fitting is merely used to approximate does this mean that the equations still hold? Any help is greatly appreciated.

 

[Sparweb]

Aerohead,

Although I don't have LSM 88 handy (I thought I did, but it's not turning up where I expected to find it), I do have a similar document from Bombardier. By looking through that one, I could see a few places where using the wrong formula - for a circular bathtub fitting instead of an angle fitting, for example - would give obviously wrong results. Also, if the geometry of your tension clip is unusual, extremely wide for example, the formula could also give a negative number.
Could you describe the goemetry more specifically? I'll keep hunting for the Memo.

Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout

 

[StressMan2506]

Hi SparWeb:

I'm one of Aerohead's colleagues and I posed the question to him which gave rise to the start of this thread.

The method for angle fittings in Lockheed Stress Memo 88a creates a notional 'bathtub' from the angle fitting. For a given set of angle fitting dimensions and hole position, it is possible for the Lockheed analogy to create a 'bathtub' where the hole centre is outside the notional fitting, or too close to the edge to encompass the whole footprint of the nut (or bolt head). My question is this: is the method valid in such cases, or should alternative approaches be used?

The Lockheed document covers 'bathtubs' and 'channels' and converts angle fittings into pseudo 'bathtubs'. Is the Bombardier document similar, or is the treatment of angle fittings independent of any other type? Is the Bombardier document available to interested parties?

 

[SuperStress]

The way I see it, having a negative value for 'd' will occur when (C+D)/2 > (A+B)/pi (notation from another source which references the Lockheed memo; I think the variables are the same.)

As I see it, the only effect this will have is on the end pad bending analysis. When computing (a-d)/r_o, (to compute end pad bending constant K1) you may end up with a value too large for the chart. At the very least, you end up with an extremely large value of end pad bending (f_bue in my notation).

My memo also adds the limitation that A/B must be less than or equal to 2 to use this method.

It sounds like the geometry of this angle fitting is pretty non-standard. If the loads are low, I probably wouldn't sweat it. If the loads are high, I'd try to get a solution by another method and compare the results.

Niu has a pretty straightforward method for analysis of angle fittings starting on p.347 of his "pink" book (Airframe Stress Analysis and Sizing).

It would be interesting to know how the two methods compare.

Good Luck.
SuperStress

 

[Sparweb]

With LSM 88 in hand (courtesy of a better-organized friend), I'm finding many differences between Bombardier's data and LM's, yet it seems that BBD has copied from LM extensively. Many things have been omitted, most notably LM's Reduction Factor is missing in BBD's stuff.
Do I understand, then that your angle fitting is similar to what's shown on LSM 88 Page 8, and that the hole is beyond the diagonal line corner-to-corner of the walls?

Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout

 

[aerohead56]

The fitting in question has an A/B ratio of less than 2, so the analysis should be acceptable to use per the limitations specified in LM 88. You are correct in pointing out that the negative d value results in a value for K1 of greater than what is on the chart, which in turn makes the bending stress larger, depending on the assumptions used to extrapolate the curve. I would assume that the analyst that wrote this analysis considers this to be conservative. However, the question still arises as to whether the method is applicable to a case like this. Also, please note that the theoretical approximation runs parallel to one of the walls of the actual fitting, not diagonally across it. On a thick section with the hole nearer the unsupported edge it is entirely possible to have a negative d value without making a fitting look too wierd.

 

[Sparweb]

I'm pretty sure I am not picturing clearly what you have. Send me a picture, please (e-mail address in my profile).
Talk of a negative value of "d" means one of two things:
We are not looking at the same Memo.
Or:
You have a computer program that gets input some values and spits out a max/min value of "d".

If the former, the document I have Stress Memo 88a, 15 December 1955, revised June 1988, with some specific pages also revised subsequently in the '90's. If the latter, then you should run a few other combinations that you have already worked out by hand to troubleshoot your software. Start with a known value of D, plus all the other geometry, and work the formulas in the right direction.

The more I look at the Bombardier sheets, the more I expect them to give a result less conservative than the LSM 88, but what testing they used to back up their omissions, I can't say (Bombardier sucked a bunch of intellectual talent out of Shorts Brothers).



Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout

 

[SuperStress]

I'm not sure that you'll ever get an authoritative answer for your question.

If you're looking for reasons to disprove the analysis, the fact that you have to extrapolate chart values to arrive at your K₁ could be reason enough.

If you're looking for ways to approve the analysis, you will likely have to rely on good engineering judgement.

The questions I would ask myself:
How critical is this? Is it primary or secondary structure?
What happens if it fails? Does it put anyone in danger?
What is the margin of safety? Did the author use plastic bending?
What about loads? How confident are you in the applied loads?
Were other miscellaneous factors used (fitting, casting, etc.) which provide additional safety?
How hard would it be to produce a rudimentary FEM to validate his stresses?

Of all these, safety has to be the #1 concern.

If the analysis produces reasonable results with high margins of safety, then it's probably okay.

On the other hand, if the author had to use every trick up his sleeve to eek out a MS=+.001, then I'd be a little cautious.

SuperStress